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LISSAJOUS KNOTS

Water Engineering & Modelling, 766 North Mentor, Pasadena, California 91104, USA

Department of Chemistry, University of California, Structural Biology Division, Lawrence Berkeley Laboratory, Berkeley, California 94720, USA

J.E.H. was supported in part by National Institutes of Health grant GM47945 and by the Office of Basic Energy Science in the Biological Energy Division of the Department of Energy under contract DE-ACO30-76F000978. J.E.H. thanks David Hearst and Georges Papadopoulos for their assistance in the graphics programming.

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V. F. R. JONES

Department of Mathematics, University of California, Berkeley, California 94720, USA

Partially supported by U.S. Air Force contract FDF 49620-92-J-0067 and National Science Foundation grant DMS 87-20208.

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, and

L. STOILOV

Department of Mathematics, University of California, Berkeley, California 94720, USA

L.S. was supported in part by National Institutes of Health grant GM 47945.

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https://doi.org/10.1142/S0218216594000095Cited by:43 (Source: Crossref)

Abstract

A Lissajous knot is defined to be one isotopic to a knot which admits a parametrization (for 0≤t≤2π)

Motivation for considering Lissajous knots came originally from the study of DNA molecular configurations. We will show that a Lissajous knot necessarily has Kervaire invariant zero so that the trefoil, figure-8 and the (2,5) torus knot are not Lissajous. The knot 5₂ can be realized with n_x = 2, n_y = 3, n_z = 7.

Vol. 03, No. 02

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History

Received 2 December 1993

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LISSAJOUS KNOTS

Abstract

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